Question

I hope some experts out there could help me obtain the right plot for this solid.

z=8-x-2y the plane is cut of by the cylinder with domain in the xy plane x^2+y^2=1

Answer 1

I have tried to set

\[8-x-2y=x^2+y^2\] this give me a parabolid and are faulty.

Preferebly someone can tell me how to obtain a solution.

Answer 2

Multivariable calculus? x,y,z plane?

Answer 3

Yeah.

\[r(t)=[r*\cos(t),r*\sin(t),plane]\]

is that a possible solution? and what is the plane? 8-r*cos(t)-2*r*sin(t)? i wanna do it general in cartesian to

Answer 4

is this correct?

Answer 5

yup, i think so


intersection is on:

\vec r = <x,y,z> = <x, y ,8 - x - 2y>\(\vec r = <x,y,z> = <x, y ,8 - x - 2y>\)

= <\cot \theta,\sin \theta,8 - \cos \theta - 2\sin \theta>, \quad t \in [0, 2\pi ]\(= <\cot \theta,\sin \theta,8 - \cos \theta - 2\sin \theta>, \quad \theta \in [0, 2\pi ]\)